Due to its importance, the gauged stu model has been extensively studied in the past. The first example appeared in [1]}, where the four-dimensional \(N=2\)  theory was obtained as a truncation of \(N=8\)  gauged supergravity, and static nonextremal black holes carrying electric or magnetic charges were presented. Subsequently, static and BPS generalizations were constructed in [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, while nonextremal solutions to the t\(^3\)  and stu models were found in [8]}, [9]}. Rotation was added in [10]}, [11]}, and more recently in [12]}, [13]}, [14]}. Moreover, in [12]} a general analysis of the possible asymptotic behaviours was performed by means of the real formulation of special geometry, in terms of a specific quartic form \(I_4\)  invariant under symplectic transformations. This provides a way to treat symplectically related prepotentials on the same footing, including theories which do not admit a prepotential. Although in the ungauged case all these theories lead to the same physics, the gauging breaks symplectic invariance, producing systems with different behaviours for the same gauge couplings, e.g. an AdS boundary at infinity or something completely different.
